2.1.

Tissue Preparation

The muscle samples were obtained from adult CD1 mice. The mice were anesthetized by ${\mathrm{CO}}_2$ narcosis, sacrificed, and the lower limbs dissected. Snips of quadriceps femoris or gastrocnemius muscles were dissected by a $4.0\text{-}\mathrm{mm}$ outer diameter $\times 80\text{-}\mathrm{mm}$ skeletal muscle biopsy needle and then sliced with a vibratome to thicknesses of 100 to $400\mu \mathrm{m}$ . These were briefly washed in PBS buffer and then immersed into clearing media. The clearing solutions contained 25, 50, or 75% glycerol, $70\mathrm{mM}$ $\mathrm{NaCl}$ , $1\mathrm{mM}$ $\mathrm{KCl}$ , $1.5\mathrm{mM}$ ${\mathrm{MgCl}}_2$ , $10\mathrm{mM}$ imidazole- $\mathrm{HCl}$ pH 7.0, $5\mathrm{mM}$ EGTA, and $1\mathrm{mM}$ PMSF. Tail tendon was dissected from adult Sprague-Dawley rats and adult CD1 mice. Rat tails were used for measurement of the bulk optical properties, as those from mice were not sufficiently large to cover the apertures of the integrating spheres. In each case, to isolate tendon fibrils, the skin was pulled from the tail, and strips of tendon collagen were carefully detached from the bones. The tendon was carefully unwrapped for integrating sphere measurements. This technique was deemed essential, as entire tendon is too thick to permit full light penetration. SHG analysis of unwrapped tendon revealed little damage to the fibrillar structure, but the process did lead to the introduction of relatively large voids, which were sporadically spaced. Thus, a best effort was made to perform measurements on uniform locations (greater than the spot size of the laser beam). It was then immersed in the same clearing solutions as muscle. Mouse tendon was used for SHG imaging, as whole rat tendons were too thick to permit imaging in the forward direction. Before imaging, the tendon was cut into smaller fragments ( $1\mathrm{cm}$ long), positioned on the microscope slide, immersed in the clearing solution, and secured under a silicone grease-mounted coverslip.

2.2.

SHG Microscope

The SHG imaging system consists of a laser scanning head (Olympus Fluoview 300) mounted on upright microscope (Olympus BX61) and coupled to a mode-locked Titanium Sapphire laser. All measurements were performed with a laser fundamental wavelength of $890\mathrm{nm}$ with average power of $\sim 5$ to $20\mathrm{mW}$ at the specimen. The microscope simultaneously collects both the forward and backward components of the SHG intensity. In the former, a long working distance $40\times 0.8\text{N.A.}$ water-immersion objective and a $0.9\text{N.A.}$ condenser provide excitation and signal collection, respectively. The backward component is collected through the excitation objective in a non-descanned configuration. In each channel, the SHG signal is isolated with a dichroic mirror and $10\text{-}\mathrm{nm}$ bandpass filter ( $445\mathrm{nm}$ , Semrock). The signals are detected by two identical photon-counting photomultiplier modules (Hamamatsu 7421). The SHG wavelength $\left(445\mathrm{nm}\right)$ was confirmed with a fiber optic spectrometer (Ocean Optics). There is no detectable autofluorescence for either collagen or muscle at this excitation wavelength.

2.3.

Image Analysis

SHG image stacks were quantitatively analyzed with ImageJ software (http://rsb.info.nih.gov/ij/). A coumarin dye slide emitting two-photon excited fluorescence at the SHG wavelength $(\sim 450\mathrm{nm})$ was used to calibrate both signal collection channels to account for uneven losses in optical paths and relative collection efficiency of the two detectors. Since the forward-to-backward (F/B) fluorescence ratio from a dye slide is assumed to be one, it becomes the normalization factor for the two collection geometries.

2.4.

Bulk Optical Parameters

The Monte Carlo simulations (see the following) require the following bulk optical parameters: scattering coefficient $\left({\mu }_s\right)$ , absorption coefficient $\left({\mu }_a\right)$ , and anisotropy $\left(g\right)$ of the tissue at the fundamental and SHG wavelengths. We determined these parameters for muscle and tendon at $457\mathrm{nm}$ ( ${\mathrm{Ar}}^{+}$ line approximating the SHG wavelength) and $890\mathrm{nm}$ (unfocused Ti:Sapphire) using the following measurements. The diffuse reflected and transmitted intensities were measured by placing the specimen ( $\sim 100\mu \mathrm{m}$ in thickness) between a dual integrating sphere setup, where the entrance and exit spheres have 3 and 2 ports, respectively. In order to avoid multiple interfaces, tissues were mounted on custom-built holders for unobstructed positioning between the spheres and kept hydrated during the measurement. The refractive indices necessary for the extraction of the scattering and absorption coefficients²⁵ were determined using the method of Li and Xie,²⁶ where the specimen is placed on a cylindrical lens and the critical angle for total internal reflection is measured. Utilizing the measured transmittance and reflectance, anisotropy factor ( $g$ assumed to be 0.96),²⁷ the index of refraction and the tissue thickness, inverse Monte Carlo simulations are utilized to determine the absorption coefficient ${\mu }_a$ , and scattering coefficient ${\mu }_s$ , which is related to the scattering coefficient ${\mu }_s^{\prime }$ by:

2.5.

Monte Carlo Simulations

For comparison with the experimental 3-D data and to decouple the respective roles of the primary and secondary inner filter effects on SHG creation and propagation, Monte Carlo simulations based on photon diffusion using the bulk optical parameters were performed. To this end, we adapted a previous model by Wang ²⁸ to calculate the escape probabilities for the forward and backward channels. The simulation requires the bulk optical parameters determined in Sec. 2.4 and tissue thicknesses. Optical sectioning is simulated by calculating the fraction of incident laser photons that arrive at the focal point at a given depth based on the $0.8\mathrm{NA}$ in conjunction with the measured value of ${\mu }_s$ at $890\mathrm{nm}$ . This simulation results in the determination of the primary filter effect on the SHG intensity (proportional to the square of the 890 transmission) at all depths in the tissue. Secondary filter effects are then modeled by calculating the propagation losses governed by the bulk optical properties at the SHG wavelength.

3.1.

Mechanism of Optical Clearing in Muscle Tissue

In our previous work, we postulated that the increase in SHG imaging depth in striated muscle arose from a reduction in the secondary inner effect, i.e., reduced absorption of the SHG as it forward-propagated through the remainder of the tissue. We now enhance this preliminary effort through knowledge of the bulk optical parameters and use of Monte Carlo simulations to unambiguously determine the optical clearing mechanisms. The results from the integrating sphere measurements for the scattering coefficient $\left({\mu }_s\right)$ and absorption coefficient $\left({\mu }_a\right)$ for the control and for glycerol concentrations of 25%, 50%, and 75% at $457\mathrm{nm}$ (SHG) and $890\mathrm{nm}$ (fundamental) are summarized in Table 1 . We assumed an anisotropy value of $g=0.96$ from the literature,²⁷ as we were unable to cut sufficiently thin sections to ensure an accurate measurement, where these would have needed to be $\sim 20\mu \mathrm{m}$ $(\sim 1∕{\mu }_s)$ to avoid convolution effects from multiple scattering. We first noted that at both wavelengths, ${\mu }_s\gg {\mu }_a$ . We further observed that treatment with glycerol greatly reduces the scattering coefficients at both wavelengths, where the effect is highly pronounced for the 50% and 75% cases, and is approximately an order of magnitude relative to the control. However, a corresponding reduction occurs with 25% glycerol application as well. The absorption coefficients also decrease with clearing, presumably due to loss of cytoplasmic proteins; however, the initial magnitudes were much smaller than those of ${\mu }_s$ . We note that these bulk optical parameters are not obtainable from the 3-D image data directly, as the depth-dependent SHG intensity is linked directly to the square of laser intensity (and thus conversion efficiency), emission directionality, and subsequent propagation losses.

Table 1

Bulk optical parameters for striated muscle at the fundamental and SHG wavelengths.

To gain further insight into the clearing mechanism, we measure the axial attenuation of the forward SHG signal as a function of glycerol concentration. This response is resultant from the combination of the primary and secondary filter effects on the SHG creation and propagation, respectively. Representative $x\text{-}z$ projections used for this analysis for the 25% and 75% glycerol are shown in the top panels in Fig. 1a . The attenuation curves, $I_{SHG}\left(z\right)$ versus $z$ are calculated as the average of 15 to 20 image stacks, and the resulting data for the control and three glycerol concentrations are shown in Fig. 1b. The data are normalized to the maximum in each image stack for each percent glycerol treatment, and the averages of these fractional glycerol treatments are then normalized to each other. Application of glycerol results in a swelling of the muscle cells, where the higher concentrations result in thicker tissues for the same exposure time. Thus, it is necessary to consider swelling in addition to bulk optical parameter changes when directly comparing the data because the physical thickness affects the subsequent measured signal attenuation and directionality. Due to decreased scattering and absorption losses, we observed that the 50% and 75% glycerol treatments result in similar axial attenuation profiles, showing reduced attenuation relative to the 25% case and control. These trends are indicative of the corresponding reduction in the measured ${\mu }_s$ values associated with optical clearing.

Fig. 1

3-D SHG imaging of cleared striated muscle tissue. (a) $x\text{-}z$ projections of the SHG image stacks for 25% (left) and 75% (right) glycerol treatments. $\mathrm{Scale}=50\mu \mathrm{m}$ . (b) The normalized axial attenuation of the forward SHG intensity for the control and three glycerol treatments. All the glycerol treatments result in greater imaging depth relative to the control.

These measured attenuation curves [Fig. 1b] cannot be represented as single exponentials, as they arise from both the primary filter effect on the laser intensity as well as the secondary filter processes directly affecting the SHG intensity. Moreover, the relative contributions of these factors are depth-dependent. Thus, to decouple the individual filter effect, we perform Monte Carlo simulations of the depth-dependent relative SHG generation and propagation using the bulk optical parameters (Table 1), comparing our final simulated SHG transmittance to the experimental data. In these simulations, we assume a fixed SHG scattering cross-sectional area, 100% forward emission directionality (see the following justification), and 100% conversion efficiency for primary photons contained within this focal volume at the prescribed penetration depth.

Figure 2a shows the square of the transmission of the laser through $200\mu \mathrm{m}$ of propagation, representing the primary filter effect alone on the resulting laser intensity and thus the relative intensity of the created SHG throughout the axial profile. The simulated curves strongly resemble the SHG attenuation data [Fig. 1b] in two important ways: First, the simulations show the similarity of the 50% and 75% glycerol cases, as well as the inbetween behavior of 25% treatment with respect to the uncleared tissue. Second, these curves also reproduce the overall curvature of the experimentally observed data, where the highly cleared tissues are more monotonic in the intensity attenuation, and the uncleared tissue and 25% cases have an inflection point in the middle of the depth response. We note that for each treatment, the rate of attenuation predicted by the simulation is more rapid than for the analogous experiment. While this could possibly arise from inaccuracies in measurement of the bulk optical parameters (dominated by ${\mu }_s$ values), we will describe in Sec. 4 that the disagreement between the experiments and simulations is largely due to differences in SHG conversion efficiencies in the treated tissues. However, for the current context, we note that these determinations were made self-consistently, and we use the resulting values in a comparative analysis between the cleared and uncleared tissues.

Fig. 2

Monte Carlo simulations of the SHG attenuation curves for the experimental cases shown in Fig. 1 using the bulk optical parameters tabulated in Table 1. Simulations of the axial dependence of the primary filter effect by calculation of the square of the transmission $\left(T^2\right)$ at $890\mathrm{nm}$ . (b) Simulation of the axial dependence of the SHG intensity arising from both primary and secondary filter effects. Comparison of these simulations with the experimental data indicates that the axial SHG response is dominated by the primary filter effect on the laser intensity.

This exercise leads to the unintuitive conclusion that the axial attenuation response is largely determined by the primary filter effect, rather than losses due to the secondary filter effects of scattering and absorption of the SHG signal. To further illustrate this comparison, the simulated SHG attenuation curves (governed by both the primary and the secondary filters) in Fig. 2b are shown to track the attenuation of the square of the laser transmittance plotted in Fig. 2a. Thus, while ${\mu }_s$ for the uncleared tissue at $890\mathrm{nm}$ $\left(285{\mathrm{cm}}^{-1}\right)$ is approximately half the $457\text{-}\mathrm{nm}$ value, it is still significant in the present case, where the $35\text{-}\mu \mathrm{m}$ mean free path (MFP; $1∕285{\mathrm{cm}}^{-1}$ ) is much less than the thickness of the tissue. Additionally, the primary filter has a quadratic effect on the SHG conversion efficiency and thus dominates the subsequent propagation loses of the second harmonic signal through the turbid media.

To further demonstrate the impact of the reduction of ${\mu }_s$ , we can also compare the experimental and simulated axial dependence of the ratio of the F/B detected SHG intensity for cleared and uncleared tissues. This response is governed by the SHG creation directionality as well as the bulk optical parameters at the SHG wavelength. The detected backward SHG is a superposition of direct quasi-coherent emission²⁹ and a multiple scattered incoherent component. In general in turbid tissue specimens, the measured signal results from both contributions,³⁰ where the relative magnitudes depend on the morphology of the tissue assembly as well as the bulk optical parameters. Previously, we assigned the myofibril as the SHG producing element,³¹ and based on our recent theoretical analysis,²⁹ the SHG creation in muscle should be essentially all forward directed. Thus, the depth dependence of the F/B ratio in muscle tissue will be governed by ${\mu }_s$ and $g$ at ${\lambda }_{SHG}$ .

Monte Carlo simulations of F/B versus z for the control and tissues cleared with three different glycerol concentrations (25%, 50%, and 75%) are shown in Fig. 3a . These simulations show that for all the tissues, the F/B increases with increasing depth into the muscle tissue and further that the overall F/B level increases with glycerol concentration (which acts to decrease the number of scattering events, thus reducing the backward signal, which predominantly arises from multiple scattering events). As also shown in Fig. 3a, the curves merge at the back side of the tissue. This result is a consequence of photon diffusion theory, where at least one MFP is required between the location of the emitted photon to the forward boundary of the specimen for efficient multiple scattering to occur.²⁸ Thus at increasing focal depths, the probability of scattering collisions is decreased as the remaining thickness becomes much shorter than the MFP, which becomes longer for the cleared tissues. The corresponding experimental data for the 25, 50, and 75% glycerol treated muscle are shown in Fig. 3b. We observe that the F/B at the top of the stack increases with glycerol concentration, where these values range from 7 to 10 and increase to $\sim 15$ at the bottom tissue exit. Thus, the experimental data qualitatively match the trends predicted by the Monte Carlo simulations assuming 100% forward SHG creation. This rise of the F/B with increasing depth delineates the effect of the secondary filters on the measured SHG signal, where these diminish with the decrease in exit path length. Based on the measured bulk optical parameters, where ${\mu }_s>{\mu }_a$ , we assign the propagation losses in all cases primarily to multiple scattering as opposed to absorption.

Fig. 3

Comparison of the axial dependence of the directionality of the SHG propagation for the control and three glycerol treatments. (a) Monte Carlo simulations of the depth-dependent forward-to-backward (F&B) ratio, assuming 100% forward creation directionality; and (b) experimental F/B data. The agreement between the experiment and simulation of the initial ratio indicate that the SHG creation directionality is 100% forward. The data for the experimental control was in the noise floor, and a meaningful F/B ratio could not be ascertained.

We note that we performed this measurement for uncleared tissue as well; however, the detected backward signal was in the noise floor for much of the depth profile, and we could not extract a meaningful F/B plot. Further confounding this measurement was the overall reduced SHG intensity relative to the cleared cases deep into the tissue [see Fig. 1b]. We attribute this effect to the large scattering coefficient at $457\mathrm{nm}$ ( ${\mu }_s\sim 500{\mathrm{cm}}^{-1}$ or MFP $\sim 20\mu \mathrm{m}$ ) in conjunction with the limited collection aperture. Thus, deep into the tissue, a fraction of the multiple scattered photons are scattered into a radius at the exit of the tissue larger than the first element of the excitation objective lens $(r\sim 1\mathrm{mm})$ , resulting in missed photons. Similarly, we attribute the crossing of the 25% curve over both the 50% and 75% in the experimental curve at deeper depths to incomplete collection of all the backscattered photons, resulting in an artificially high F/B. The tissues cleared with higher glycerol concentrations do not suffer from this effect, as their associated photon trajectories are more on-axis.

Good agreement between the experimental and theoretical F/B data (approximately 10:1) at the top of the 3-D image stacks is attributed to the validity of our theoretical assumption that SHG creation is essentially forward, which also has been found in other experimental observations.³² This emission directionality is a physically interpretable result, as the myofibril (i.e., the SHG-producing elements) diameters are on the order of a micron, and based on theoretical predictions,^{24, 29} SHG-creating structures on this size scale or larger than ${\lambda }_{SHG}$ result in near 100% forward emission. By contrast, if appreciable initial backward emission occurred, a smaller F/B would be observed experimentally at all depths until the exit of the tissue.³⁰

3.2.

Optical Clearing in Tendon

As SHG imaging of collagenous tissues in conjunction with optical clearing has great potential, the combined use of these techniques warrants further investigation. Here, we explore the mechanism and capabilities of optical clearing in 3-D imaging of tendon by making quantitative assessments of the imaging depths and intensities and subsequent modeling of these effects by Monte Carlo simulation of the SHG creation and propagation. Tendon is an ideal candidate for these studies due to the highly regular fibril structure as well as its homogeneous composition.

Figure 4a shows $x\text{-}z$ projections of 50% glycerol treated mouse-tail tendon immediately (left) and then $5\mathrm{h}$ (right) after immersion. We note that while these cross sections are similar in appearance in terms of the collagen assembly, the cleared tissue exhibits significant swelling. The cross-sectional area of the tendon over $5\mathrm{h}$ of immersion is plotted in Fig. 4b, showing an approximately 2.2-fold increase. We note that while the increase in the fibril spacing is below resolution of the microscope, it is manifested in decreased intensity in single optical sections due to a decrease in the local concentration of “harmonophores.”

Fig. 4

3-D SHG imaging of 50% glycerol treated tendon. (a) $x\text{-}z$ projections of the SHG image stacks for $15\min$ (left) and $5\mathrm{h}$ (right) after immersion. $\mathrm{Scale}=50\mu \mathrm{m}$ . Significant swelling is observed. (b) Resulting cross-sectional area over a $5\text{-}\mathrm{h}$ time course. The area increases by approximately twofold.

As the tissue remains intact and does not appear damaged following this expansion, an interesting question then regards the effect of clearing on the overall SHG intensity. We measured the resulting intensity through an entire cross section over a $5\text{-}\mathrm{h}$ time course, and the results are shown in Fig. 5 , where a $\sim 2$ -fold enhancement in the integrated SHG intensity is observed. We stress that this increase in SHG intensity occurs over the volume of the swelled tissue, where, by contrast, the intensities in individual optical sections are lower. We believe that the overall increase in integrated volumetric SHG intensity is indicative of the retention of morphological structure through the clearing process, although swelling is present. Moreover, the clearing process was reversible upon washing out the glycerol with PBS, furthering our conclusion that the tissue structure was not detrimentally altered. This point is illustrated in Fig. 6 , showing the 3-D rendered image stacks from precleared (a), cleared (b), and reversed (c) tendon.

Fig. 5

3-D integrated SHG intensity for the time course shown in Fig 4. The overall SHG increases by twofold, despite the lower intensity in single optical sections.

Fig. 6

The clearing in tendon with 50% glycerol is reversible. The 3-D renderings are for the SHG of (a) uncleared tendon, (b) cleared tendon, and (c) tendon following washing in PBS. Scale $\mathrm{bar}=20\mu \mathrm{m}$ .

To interpret these data, we measured the bulk optical parameters for control and 50% glycerol treated tendon at the fundamental and SHG wavelengths, and the results are shown in Table 2 . We observe that the scattering coefficients drop dramatically, e.g., almost 20-fold at ${\lambda }_{SHG}$ upon clearing. This presumably arises from replacing interfibril water with the index-matching glycerol, where this results in increasing the interfibril spacing as well.

Table 2

Bulk optical parameters for tendon at the fundamental and SHG wavelengths.

This reduction of scattering is also reflected in the SHG forward attenuation data. Figure 7 shows this data for the control and 25, 50, and 75% glycerol treated tendon, where the tissues were cleared for $12\mathrm{h}$ . The imaging depth in each case represents the physical thickness of the tendons before and after clearing. As in the case of muscle, the rates of attenuation are much slower with respect to depth for the increasingly cleared tissues. For example, the 75% treatment is the most dramatic case and exhibits a nearly flat response over $\sim 200\mu \mathrm{m}$ of depth into the tissue.

Fig. 7

The normalized axial attenuation of the forward SHG intensity for the control and three glycerol treatments for tendon after $12\mathrm{h}$ of immersion. Increasing the glycerol fraction results in increased swelling as well as a decrease in the rate of the axial attenuation.

To determine whether the integrated increase in SHG intensity (Fig. 5) is consistent with reduction in ${\mu }_s$ , we performed analogous Monte Carlo simulations of the SHG forward attenuation as was done for the muscle tissue. Here, we perform the comparison at $5\mathrm{h}$ post-immersion. The experimental data and simulations for the control and 50% are shown in Figs. 8a and 8b , respectively, and the trends are in qualitative agreement. Namely, the SHG for the uncleared tissue experiences a rapid attenuation through $100\mu \mathrm{m}$ in both the experimental data and the simulation. The experimental and simulation results for the 50% case are similar, where the SHG intensity decreases are approximately 20% and 5%, respectively. This difference in the experiment and the simulation probably arises from the large variability in measuring absolute values of the scattering coefficient variations in the sample preparation, which involves unrolling the tendon fibrils, as was required for experimental compatibility. However, we use these ${\mu }_s$ values only for comparative analysis, and the fact that the trends in the data and modeling are similar indicates greatly reduced scattering in the cleared tissue relative to the control. As a further comparison, we can estimate the overall enhancement of the SHG throughout the 3-D volume by integrating the areas under the curves. This analysis results in an overall intensity increase of factors of 2.2 and 3 for the experiments and simulations, respectively, and thus is in qualitative agreement. Therefore, 3-D imaging and modeling allows us to conclude that optical clearing in tendon does indeed increase the SHG intensity to the extent predicted by the reduction of scattering.

Fig. 8

Comparison of the experimental (a) and simulated (b) axial response of tendon before and after 50% glycerol treatment $5\mathrm{h}$ post-immersion. Integration under the curves reflects the entire SHG intensity before and after clearing, where the experiment and simulations show overall SHG enhancement factors of two- and three-fold, respectively. These results indicate that the measured increase in SHG is consistent with the decrease in scattering measured with integrating spheres.